## Quantitatively assessing flow velocity by the slope of the inverse square of the contrast values versus camera exposure time |

Optics Express, Vol. 22, Issue 16, pp. 19327-19336 (2014)

http://dx.doi.org/10.1364/OE.22.019327

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### Abstract

The slope of the inverse square of the contrast values versus camera exposure time at multi-exposure speckle imaging (MESI) can be a new indicator of flow velocity. The slope is linear as the diffuse coefficient in Brownian motion diffusion model and the mean velocity in ballistic motion model. Combining diffuse speckle contrast analysis (DSCA) and MESI, we demonstrate theoretically and experimentally that the flow velocity can be obtained from this slope. The calculation results processes of the slop don’t need tedious Newtonian iterative method and are computationally inexpensive. The new indicator can play an important role in quantitatively assessing tissue blood flow velocity.

© 2014 Optical Society of America

## 1. Introduction

1. A. Fercher and J. Briers, “Flow visualizaiton by means of single-exposure speckle photography,” Opt. Commun. **37**(5), 326–330 (1981). [CrossRef]

2. J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. **1**(2), 174–179 (1996). [CrossRef] [PubMed]

3. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. **31**(12), 1824–1826 (2006). [CrossRef] [PubMed]

5. Z. Wang, S. Hughes, S. Dayasundara, and R. S. Menon, “Theoretical and experimental optimization of laser speckle contrast imaging for high specificity to brain microcirculation,” J. Cereb. Blood Flow Metab. **27**(2), 258–269 (2007). [CrossRef] [PubMed]

6. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. **76**(9), 093110 (2005). [CrossRef]

*s*refers to the spatial or to temporal [3

3. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. **31**(12), 1824–1826 (2006). [CrossRef] [PubMed]

7. H. Cheng, Y. Yan, and T. Q. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express **16**(14), 10214–10219 (2008). [CrossRef] [PubMed]

8. R. Bi, J. Dong, and K. Lee, “Deep tissue flowmetry based on diffuse speckle contrast analysis,” Opt. Lett. **38**(9), 1401–1403 (2013). [CrossRef] [PubMed]

9. R. Bi, J. Dong, and K. Lee, “Multi-channel deep tissue flowmetry based on temporal diffuse speckle contrast analysis,” Opt. Express **21**(19), 22854–22861 (2013). [CrossRef] [PubMed]

10. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. **60**(12), 1134–1137 (1988). [CrossRef] [PubMed]

*K*

^{2}vs. camera exposure time (T) at multi-exposure speckle imaging (MESI) [14

14. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express **16**(3), 1975–1989 (2008). [CrossRef] [PubMed]

*K*

^{2}vs. T (

*k*) changing over exposure time depends on source-detector distance, flow information and optical parameters of medium (the absorption coefficient

_{slope}*μ*, the scattering coefficient

_{a}*μ*and anisotropy parameter

_{s}*g*et al.). When the ratio of the minimum exposure time to the correlation time is much more than 1,

*k*is in linear relationship with the diffuse coefficient (

_{slope}*D*) in Brownian motion diffusion model and the mean velocity (

_{B}*v*) in ballistic model (random flow and shear flow [15

15. X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B **7**(1), 15–20 (1990). [CrossRef]

*k*can become a quantitative indicator for tissue blood flow velocity. The new indicator has more advantages and can play an important role in quantitatively assessing tissue blood flow velocity.

_{slope}## 2. Theory

### 2.1 Diffuse speckle contrast analysis

16. D. Boas and A. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A **14**(1), 192–215 (1997). [CrossRef]

*k*

_{0}is the wavenumber of the light in medium,

*S*(

*r*) is the light-source distribution and

*τ*.

17. Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, and P. Sheng, “Wave transport in random media: The ballistic to diffusive transition,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **60**(4), 4843–4850 (1999). [CrossRef] [PubMed]

18. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. **73**(7), 076701 (2010). [CrossRef]

*d*is the thickness of slab medium,

*l*is the transport mean free path,

_{tr}*R*is effective reflection coefficient to account for the index mismatch between media and surrounding medium,

_{eff}*n*=

*n*/

_{in}*n*is the ratio of the index of refraction inside and outside the diffusing medium,

_{out}*m*is an integer,

*r*is source-detector distance in x-y plane and

*z*is along the thickness direction of slab medium. A scheme of the geometry together with a description of some of the notations is shown in Fig. 1.

*ξ*

_{±}

_{m}_{, ±}

*is constant at the fixed source-detector distance and depends on*

_{x}*r*

_{±}

*,*

_{m}*r*

_{±}

*and*

_{x}*G*

_{1}(

*r, z*, 0).

*is the sum of the similar function form*g 1 ( r , z , τ )

6. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. **76**(9), 093110 (2005). [CrossRef]

*is the sum of the similar function form*g 1 ( r , z , τ )

6. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. **76**(9), 093110 (2005). [CrossRef]

*V*(

*T*) of Brownian motion and ballistic motion can be simplified to the same following expression

*K*

^{2}(

*T*) is given by

*K*

^{2}(

*T*) has a linear relationship with

*K*

^{2}(

*T*) vs T (

*k*) depends on the source-detector distance, flow information and optical parameters of medium. When the source-detector distance is constant,

_{slope}*k*has a linear relationship with diffuse coefficient

_{slope}*D*in Brownian motion and mean velocity

_{B}*v*in ballistic motion.

*k*can be used as the new indicator for quantitatively assessing flow index.

_{slope}### 2.2 Monte Carlo simulation

*K*

^{2}(

*T*) become smaller than the analytical values calculated by diffusion approximation. However, we can clearly find that the functions of 1/

*K*

^{2}(

*T*) both have a linear relationship with

*T*for ballistic motion over a broad range.

## 3. Experimental set-up

*λ*= 632.8

*nm*, 30

*mW*, Carlsbad California, USA) with a long coherence length is vertically entering the rectangular vessel (2

*cm*height and

*d*= 2

*cm*wide in cross section). The intralipid solution with a concentration of 0.15% is pumped through the polyethylene tubing (4.8

*mm*inner diameter), at different mean flow velocities and different exposure times. The optical properties of the flow phantom are

*μ*= 2

^{’}_{s}*cm*

^{−1}and

*μ*= 0.01

_{a}*cm*

^{−1}, which satisfy

*μ*>>

^{’}_{s}*μ*, and the diffusion approximation is valid.

_{a}*mm*/

*s*to 2.40

*mm*/

*s*, drived by a digital peristaltic pump. The exposure time is set at 0.3

*ms*, 0.5

*ms*, 0.8

*ms*, 1

*ms*, 2

*ms*and 3

*ms*. The transmission speckle is imaged using a prime lens, 120

*mm*lens tube and a CCD (Microvision MV-VS141FM/C; 12 bits, pixel size 4.65

*μm**4.65

*μm*, resolution ratio 1392*1040). The imaging system has a magnification of 1.7. The detector position is set at the position

*z*= 2.0

*cm r*= 0.2

*cm*.

## 4. Results and discussion

*K*.

_{s}*K*is calculated from every segment of 101 × 101 pixels for reducing the noise in laser speckle correlation [12

_{s}12. S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express **18**(14), 14519–14534 (2010). [CrossRef] [PubMed]

*K*are averaged for each exposure time and each mean velocity.

_{s}*mm*/

*s*, 1.60

*mm*/

*s*and 2.40

*mm*/

*s*corresponding to the black, the red and the blue curves respectively. If we expect to obtain the linear relationship in correlation time

*τ*, we need nonlinearly fit the contrast by MESI equation. However,

_{c}*β*is one of the unknown quantities and mainly depends on the experiment conditions. Usually we obtain

*β*by calculating the contrast of the reflectance static speckle. Holding

*β*constant, we make the nonlinear fitting to obtain

*τ*. This calculation processes need tedious Newtonian iterative method and are computationally inexpensive. Meanwhile, to improve the signal to noise ratio (SNR), the number of exposure time must be adequate. This process is cumbersome.

_{c}*k*at different mean velocities as shown in Table 1and Fig. 6(a).We can clearly find that

_{slope}*k*varies linearly with the scattering particle flow velocity. For eliminating the influence of

_{slope}*β*and plotting on the same scale in an image, the normalization is performed with respect to

*k*of the experiment results and the analytical results at their respective median values as shown in Table 1. The normalization process is performed for the different mean velocities in the same way to observe easily this linear relationship between the slope and the mean velocity.

_{slope}*k*of experiment results and the analytical results fit well. The median mean velocity can be regarded as the baseline measure value, so we can utilize this linear relationship to obtain other quantitative velocity information.

_{slope}*k*can be a new indicator to quantitatively assesse flow velocity.

_{slope}## 5. Conclusion

*k*to measure quantitatively mean velocity. The calculation theory is based on diffuse speckle contrast analysis (DSCA) and multi-exposure speckle imaging (MESI). We demonstrate that we are able to use the linear relation to fit the inverse square of the contrast values (1/

_{slope}*K*

^{2}) at different exposure times.

*k*is in linear relationship with the mean velocity. We provide MC simulation results and experiment results in a liquid phantom with varying flow velocity in the transmission geometry. The results are in support of our theory.

_{slope}## Acknowledgment

## References and links

1. | A. Fercher and J. Briers, “Flow visualizaiton by means of single-exposure speckle photography,” Opt. Commun. |

2. | J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. |

3. | P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. |

4. | K. Murari, N. Li, A. Rege, X. Jia, A. All, and N. Thakor, “Contrast-enhanced imaging of cerebral vasculature with laser speckle,” Appl. Opt. |

5. | Z. Wang, S. Hughes, S. Dayasundara, and R. S. Menon, “Theoretical and experimental optimization of laser speckle contrast imaging for high specificity to brain microcirculation,” J. Cereb. Blood Flow Metab. |

6. | R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. |

7. | H. Cheng, Y. Yan, and T. Q. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express |

8. | R. Bi, J. Dong, and K. Lee, “Deep tissue flowmetry based on diffuse speckle contrast analysis,” Opt. Lett. |

9. | R. Bi, J. Dong, and K. Lee, “Multi-channel deep tissue flowmetry based on temporal diffuse speckle contrast analysis,” Opt. Express |

10. | D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. |

11. | H. Cheng and T. Q. Duong, “Simplified laser-speckle-imaging analysis method and its application to retinal blood flow imaging,” Opt. Lett. |

12. | S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express |

13. | P.-A. Lemieus and D. J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions,” J. Opt. Soc. Am. A |

14. | A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express |

15. | X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B |

16. | D. Boas and A. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A |

17. | Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, and P. Sheng, “Wave transport in random media: The ballistic to diffusive transition,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

18. | T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. |

19. | L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. |

20. | L. Wang and S. L. Jacques, http://omlc.ogi.edu/software/mc/. |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(290.1990) Scattering : Diffusion

(290.4210) Scattering : Multiple scattering

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 3, 2014

Revised Manuscript: July 22, 2014

Manuscript Accepted: July 26, 2014

Published: August 4, 2014

**Virtual Issues**

Vol. 9, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Jialin Liu, Hongchao Zhang, Zhonghua Shen, Jian Lu, and Xiaowu Ni, "Quantitatively assessing flow velocity by the slope of the inverse square of the contrast values versus camera exposure time," Opt. Express **22**, 19327-19336 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-16-19327

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### References

- A. Fercher and J. Briers, “Flow visualizaiton by means of single-exposure speckle photography,” Opt. Commun.37(5), 326–330 (1981). [CrossRef]
- J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt.1(2), 174–179 (1996). [CrossRef] [PubMed]
- P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett.31(12), 1824–1826 (2006). [CrossRef] [PubMed]
- K. Murari, N. Li, A. Rege, X. Jia, A. All, and N. Thakor, “Contrast-enhanced imaging of cerebral vasculature with laser speckle,” Appl. Opt.46(22), 5340–5346 (2007). [CrossRef] [PubMed]
- Z. Wang, S. Hughes, S. Dayasundara, and R. S. Menon, “Theoretical and experimental optimization of laser speckle contrast imaging for high specificity to brain microcirculation,” J. Cereb. Blood Flow Metab.27(2), 258–269 (2007). [CrossRef] [PubMed]
- R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005). [CrossRef]
- H. Cheng, Y. Yan, and T. Q. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express16(14), 10214–10219 (2008). [CrossRef] [PubMed]
- R. Bi, J. Dong, and K. Lee, “Deep tissue flowmetry based on diffuse speckle contrast analysis,” Opt. Lett.38(9), 1401–1403 (2013). [CrossRef] [PubMed]
- R. Bi, J. Dong, and K. Lee, “Multi-channel deep tissue flowmetry based on temporal diffuse speckle contrast analysis,” Opt. Express21(19), 22854–22861 (2013). [CrossRef] [PubMed]
- D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett.60(12), 1134–1137 (1988). [CrossRef] [PubMed]
- H. Cheng and T. Q. Duong, “Simplified laser-speckle-imaging analysis method and its application to retinal blood flow imaging,” Opt. Lett.32(15), 2188–2190 (2007). [CrossRef] [PubMed]
- S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express18(14), 14519–14534 (2010). [CrossRef] [PubMed]
- P.-A. Lemieus and D. J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions,” J. Opt. Soc. Am. A16(7), 1651–1664 (1999). [CrossRef]
- A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express16(3), 1975–1989 (2008). [CrossRef] [PubMed]
- X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B7(1), 15–20 (1990). [CrossRef]
- D. Boas and A. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A14(1), 192–215 (1997). [CrossRef]
- Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, and P. Sheng, “Wave transport in random media: The ballistic to diffusive transition,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics60(4), 4843–4850 (1999). [CrossRef] [PubMed]
- T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73(7), 076701 (2010). [CrossRef]
- L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed.47(2), 131–146 (1995). [CrossRef] [PubMed]
- L. Wang and S. L. Jacques, http://omlc.ogi.edu/software/mc/ .

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